Evaluating the Performance of Autoregressive Model for Solar Radiation Forecasting

The solar radiation data taken from 14 meteorological stations in Nigeria has been analyzed. The periodic component of the data which covered a period of 13 (mostly 1977-1989) years was removed via Fourier analysis while the residual series was subjected to autoregressive analysis. It was evident from the t-test and autocorrelation plots of the modified (i.e. without the periodic component) series that there exist significant persistence at nine stations including Sokoto, Nguru, Kano, Maiduguri, Bauchi, Yola, Minna, Ibadan, and Benin. The autocorrelation at Jos, Bida, Ikeja, Enugu and Port Harcourt were however found to be insignificant. As the sample partial autocorrelation function cuts off after lag 1, a non-seasonal autoregressive model of order 1, AR (1), was identified for stations with autocorrelation. The Q-statistic of error series suggested that the models were adequate as identified. Moreover, the exploratory plots of the model residual series showed agreement with the quantitative statistics and thus enforces the inference that the models were adequate for monthly mean daily global solar radiation forecasts at some of the study stations. It is interesting to note that all the stations within the sub-sahelian region showed significant persistence whereas all the stations in the coastal region except Benin were found with insignificant autocorrelation. Expectedly, the performance evaluation of the model gave impressive result for the stations within the sub-sahelian region but a relatively weak result for the coastal region. The result for the midland region was mixed whereas it was difficult to conclude on the Guinea savannah region with result from only one station.

An Improved STL-LSTM Model for Daily Bus Passenger Flow Prediction during the COVID-19 Pandemic

The COVID-19 pandemic is a significant public health problem globally, which causes difficulty and trouble for both people’s travel and public transport companies’ management. Improving the accuracy of bus passenger flow prediction during COVID-19 can help these companies make better decisions on operation scheduling and is of great significance to epidemic prevention and early warnings. This research proposes an improved STL-LSTM model (ISTL-LSTM), which combines seasonal-trend decomposition procedure based on locally weighted regression (STL), multiple features, and three long short-term memory (LSTM) neural networks. Specifically, the proposed ISTL-LSTM method consists of four procedures. Firstly, the original time series is decomposed into trend series, seasonality series, and residual series through implementing STL. Then, each sub-series is concatenated with new features. In addition, each fused sub-series is predicted by different LSTM models separately. Lastly, predicting values generated from LSTM models are combined in a final prediction value. In the case study, the prediction of daily bus passenger flow in Beijing during the pandemic is selected as the research object. The results show that the ISTL-LSTM model could perform well and predict at least 15% more accurately compared with single models and a hybrid model. This research fills the gap of bus passenger flow prediction under the influence of the COVID-19 pandemic and provides helpful references for studies on passenger flow prediction.

Modeling the Risk of Extreme Value Dependence in Chinese Regional Carbon Emission Markets

In this study, we analyze the risk of extreme value dependence in Chinese regional carbon emission markets. After filtering the daily return data of six carbon markets in China using a generalized autoregressive conditional heteroscedasticity (GARCH) model, we obtain the standardized residual series. Next, the dependence structures in the markets are captured by the Copula function and the Extreme Value theory (EVT). We report high peaks, heavy tails and fluctuation aggregation in the logarithm return series of the markets, as well as significant dependent structures. There are significant extreme value risks in Chinese regional carbon markets, but the risks can be mitigated through appropriate portfolio diversification.

Study on the Sensitive Factors of Structural Nonlinear Damage Based on the Innovation Series

Constructing a damage-sensitive factor (DSF) is one of the key steps in structural damage detection. In this paper, innovation series extracted from the auto-regressive conditional heteroscedasticity (ARCH) model are proposed to construct a DSF, which is defined as the standard deviation of innovation (SDI). A three-story shear building structure is used to demonstrate and verify the performance of the proposed method, and the results are compared with the standard deviation of the residuals (SDR) based on an auto-regressive (AR) model. In the proposed method, the AR model is established using the acceleration responses obtained from the reference and test states. The residual series are then extracted for fitting the SDR. Subsequently, the ARCH model is constructed based on the residual series from the AR model, and a new DSF of SDI is defined. This study focuses on analyzing the accuracy of fitting AR model and ARCH model to vibration response data via the normal probability distribution, and identifying the characteristics of the residual and innovation series. The mean squared error (MSE) is used as the loss function to calculate the loss on residual and innovation series from the AR model and ARCH model, respectively. The results demonstrate that the SDR can be used for nonlinear damage detection. However, the proposed SDI can provide more accurate nonlinear damage identification and is robust to varying environmental condition and small damages. Thus, the innovation series developed based on ARCH model are promising for expressing and constructing nonlinear DSFs.

A cointegration approach for cable anomaly warning based on structural health monitoring data: An application to cable-stayed bridges

For long-span cable-stayed bridges, cables are one of the most important components to resist various actions. With the application of structural health monitoring technique, real-time recording of cable forces is achieved, and hence, the warning system on cable anomaly established. However, it is still difficult and there are challenges to conduct the warning system effectively, especially due to the phenomena of false alarm or omission. A practical reason is the warning index’s sensitivity to the ambient environment. Temperature variations, for instance, usually disturb the force-based cable anomaly warning and result in the false evaluation of structural condition. In view of eliminating the effects of environmental temperature, cointegration, a statistical concept from econometrics, is employed in cable anomaly warning studies. An approach that extracts warning index by linear combination of two non-stationary time series using the cointegration algorithm is developed in order to produce a more stationary cointegrated residual series (warning index series). The calculated stationary relationship between two time series is insensitive to the influence of environmental temperature and is capable of cable anomaly warning. Specifically, the framework of the cable anomaly warning system is first proposed. Subsequently, time-series test methods are introduced to check the non-stationary order and calculate the cointegration parameters of measured cable forces and environmental temperature. The computed cointegrated residual series is fed into statistical analysis as a warning index and the procedure of cable anomaly warning under the influence of environmental temperature is illustrated in detail. Finally, a case study for a cable-stayed bridge is demonstrated with results and discussions.

A Sequential Autoencoder for Teleconnection Analysis

Many aspects of the earth system are known to have preferred patterns of variability, variously known in the atmospheric sciences as modes or teleconnections. Approaches to discovering these patterns have included principal components analysis and empirical orthogonal teleconnection (EOT) analysis. The latter is very effective but is computationally intensive. Here, we present a sequential autoencoder for teleconnection analysis (SATA). Like EOT, it discovers teleconnections sequentially, with subsequent analyses being based on residual series. However, unlike EOT, SATA uses a basic linear autoencoder as the primary tool for analysis. An autoencoder is an unsupervised neural network that learns an efficient neural representation of input data. With SATA, the input is an image time series and the neural representation is a unidimensional time series. SATA then locates the 0.5% of locations with the strongest correlation with the neural representation and averages their temporal vectors to characterize the teleconnection. Evaluation of the procedure showed that it is several orders of magnitude faster than other approaches to EOT, produces teleconnection patterns that are more strongly correlated to well-known teleconnections, and is particularly effective in finding teleconnections with multiple centers of action (such as dipoles).

Аccounting for autocorrelation in a linear regression problem on an example of analysis of atmospheric column NO2 content

A method is proposed for taking into account a serial correlation (an autocorrelation) of data in a linear regression problem, which allows accounting for the autocorrelation on long scales. A residual series is presented as an autoregressive process of an order, k, that can be much larger than 1, and the autocorrelation function of the processes is calculated by solving the system of the Yule–Walker equations. Given the autocorrelation function, the autocorrelation matrix is constructed which enters the formulas for estimates of regression coefficients and their errors. The efficiency of the method is demonstrated on the base of the multiple regression analysis of data of 26-year measurements of the column NO2 contents at the Zvenigorod Research Station of the Institute of Atmospheric Physics. Estimates of regression coefficients and their errors depend on the autoregression order k. At first the error increases with increasing k. Then it approaches its maximum and thereafter begins to decrease. In the case of NO2 at the Zvenigorod Station the error more than doubled in its maximum compared to the beginning value. The decrease in the error after approaching the maximum stops if k approaches the value such that the autoregressive process of this order allows accounting for important features of the autocorrelation function of the residual series. Estimates have been obtained of seasonally dependent linear trends and effects on NO2 of nature factors such that the 11-year solar cycle, the quasi-biennial oscillation, the North Atlantic Oscillation and other.

Tidal and storm surges levels variation at the Cape Kamenny (Gulf of the Ob)

Sea level observations obtained in various expeditions since 1936, as well as those made at the polar station on Cape Kamenny (the Ob Bay) from 1952 to 1994 were subjected to treatment and harmonic analysis using the least squares method (AARI version).The aim of the work was to assess the quality of hourly and 6-hourly intervals series of sea level data and to bring these data to uniform rows for the subsequent study of tidal and surge waves. As a result of this analysis, 6-hourly interval observations of 1952–1961 were considered of low quality and not suitable for further consideration in the work. Bringing 6-hourly interval observations for 1977–1994 to uniform rows was carried out first with the control of the height basis and binding to the Baltic system of heights, and then with the help of the tide calibration method the final cast was made. In the area of tidal fluctuations of the level, erroneous information about the tide, obtained during the treatment of observations for 1936, which were placed in the tide tables for 1941, was revealed. New average estimates of harmonic constants for the summer period were proposed. The study of surges of level is based on uniform series, as well as residual ones (observations minus predictions). At the same time, the tide calculation (prediction) was made according to the program developed at AARI for the average monthly values of harmonic constants (12 sets of tides lists in the annual cycle) with the inclusion of long-period tides. Statistical quantitative characteristics of non-periodic level fluctuations were obtained for the total and residual series of observations. They are calculated on a unique hourly series for the years 1947–1948. And 6-hourly interval data for 1977–1994. For the estimation of surges, the level above 5 % of estimation was used, and the drifts were distinguished by the level below 95 % of estimation. Relationships are obtained between the duration and rate of growth of the level during surges, as well as the decline and rise of the level during drifts.